The most common and most likely answer to this crossword clue is the 4 plus 5 letter word BETE NOIRE
I've seen this crossword clue in Financial Times
B
E
T
E
N
O
I
R
E
More clues leading to the result BETE NOIRE
- Speculation I rejected with fury as anathema
- Be sure Ireland will shelter no undesirable
- Wager Ireland should brook no abomination
- Wager Irish Republic will shelter no undesirable
- Speculate one will return with anger, seeing pet aversion
- Free beer on site, but no seconds, is an anathema
- Gamble on Eire developing a particular pet hate
- Anathema to risk single! Rejected with indignation
- Nobody likes this black beast
Buddy explains!
The straight part
We know that "undesirable" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case undesirable = bete noire.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.